I have a new dimmer switch that to replace an old standard light switch. The old switch has 4 cables coming into it as in the picture. and the new one purchased from amazon is Lutron GL-600H-DK. It has 2 black wires and 1 green as in the picture. I watched some videos on youtube but still have doubts on which wires go with which and where does the extra black wire in the in the old switch go? And would this work with standard light bulbs?
Edit: From your picture and descriptions you appear to have a three way switch.
Your dimmer is a single pole dimmer. Meaning it is designed to operate in one location.
A Lutron three way dimmer that is similar to what you have would have one red, one red/white striped, one solid black, and a green.
The two blacks off the switch wire to the black on the dimmer. The one red goes to red, the one black goes to the red/white striped off the dimmer, and the green goes to the bare copper.
Be sure to turn off power first, and make sure the dimmer is rated for the correct load: Incandescent, LEDs, total wattage.